Barclays, Lloyds TSB and NatWest came bottom of an annual customer satisfaction survey from the Consumers' Association's Which? magazine, while HSBC was rated as average.
In contrast, the survey, based on responses from 4,321 members of the association, found that online and telephone banks such Smile and First Direct - a wholly owned subsidiary of HSBC - achieved high satisfaction ratings because of competitive interest rates and good customer service.
Only 30% of Lloyds TSB customers were "very satisfied", compared with 80% of Smile customers. Barclays and NatWest fared little better at 35% and 31% respectively.
Ashleye Sharpe, head of money research at Which?, said the big four banks could not afford to ignore the threat of smaller Internet rivals. "These results make a mockery of the big four's claim that they compete on service and so do not need to offer good rates," she said.
"They have shown no improvement in customer service. This should be a spur to anyone considering switching their accounts away from the big four," Sharpe added.
Consumer perception that it is too difficult to switch bank accounts is changing. Earlier this year, a Which? survey found 73% of people who had switched current accounts from the big four had found it easy.